Co-operative Populations of Neurons: Mean Field Models of Mesoscopic Brain Activity

While the basic units of computation in the brain are the neuronal cells, their sheer number, complexity of structural organisation and widespread connectivity make it difficult, if not impossible, to perform realistic simulations of activity at millimetre range or beyond. Furthermore, it is becoming increasingly clear that a range of non-neuronal and stochastic factors influence neuronal excitability, and must be taken into account when developing models and theories of brain function. One answer to the these persistent difficulties is to model cortical tissue not as a network of spike-based enumerable neurons, but to take inspiration from statistical physics and model directly the bulk properties of the populations constituting the cortical tissue. Such an approach proves compatible with many experimental recording techniques and has led to a successful class of so-called “mean field theories” that, when constrained by meaningful physiological and anatomical parameterisations, reveal a rich repertoire of biologically plausible and predictive dynamics. The aim of this chapter is to outline the historical genesis of this important modelling framework, and to detail its many successes in accounting for the experimentally observed neuronal population activity in cortex.